## Algebra

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Question 1 |

If x

^{3}+ y^{3}= 9 and x + y = 3, then the value of x^{4}+y^{4}is,21 | |

0 | |

17 | |

25 |

**Algebra**

**Discuss it**

Question 1 Explanation:

x^{3}+y^{3}= (x + y) × (x^{2}− xy + y^{2}) Putting given values of x^{3}+y^{3}and (x + y) 9 = 3 × ((x+y)^{2}− 3xy) = 3 × (9 − 3xy) = 27 − 9xy 9xy = 18 xy = 2 x^{4}+ y^{4}= (x^{2}+ y^{2})^{2}- 2x^{2}y^{2}= (x^{2}+ y^{2})^{2}- 2*4 [Putting value of xy] = ((x^{}+ y^{})^{2}- 2xy)^{2}- 2*4 [Putting values of (x+y) and xy] = (9 - 4)^{2}- 2*4 = 17

Question 3 |

For any real number x the maximum value of 4−6x−x

^{2}is at x=,4 | |

6 | |

-3 | |

3 |

**Algebra**

**Discuss it**

Question 3 Explanation:

Differentiate and equate to 0
6+2x =0
x=−3

Question 4 |

If 5

^{√x}+12^{√x}=13^{√x}then value of x is,2 | |

1 | |

3 | |

4 |

**Algebra**

**Discuss it**

Question 4 Explanation:

say x=1

17!=13

for, x=2 and 3 also not possible

x=4

52+122=132

169=169

17!=13

for, x=2 and 3 also not possible

x=4

52+122=132

169=169

Question 9 |

6 | |

2 | |

3 | |

0 |

**Algebra**

**Discuss it**

Question 9 Explanation:

Put -ac = ab + bc ; -ab = ac+ bc and -bc =ab + ac

(ab + bc + ca)/[(a+b+c)(abc)]

as, ab+bc+ca=0

= 0

(ab + bc + ca)/[(a+b+c)(abc)]

as, ab+bc+ca=0

= 0

Question 10 |

Following instructions are to be used throughout the quiz:
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read both the statements and
Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer (e) if the data in both Statements I and II together are necessary to answer the question.
If x,y are integers, then (x

^{2}+ y^{2})^{1/2}is an integer? I) x^{2}+ y^{2}is an integer II) x^{2}- 3y^{2}= 0A | |

B | |

C | |

D | |

E |

**Algebra**

**Data Sufficiency**

**Discuss it**

There are 16 questions to complete.